Improved Locally Linear Embedding by Using Adaptive Neighborhood Selection Techniques

Unsupervised learning algorithm locally linear embedding (LLE) is a typical technique which applies the preserving embedding method of high dimensional data to low dimension. The number of neighborhood nodes of LLE is a decisive parameter because the improper value will affect the manifold structure in the local neighborhood and lead to the lower computational efficiency. Based on the fact that the shortest path in low-density can be established easily, this paper proposes an improved LLE method by using the sparse matrix in combination with the weights related to each point used for the linear combination in local neighborhood. The correlation dimension between high and low dimension is used to estimate the proper number of the reduced dimension, thereby selecting the best upper bound for the non-uniform manifold. Finally, we provide the experimental evaluation to verify the effectiveness of the proposed algorithm.